Is REINFORCE the same as 'vanilla policy gradient'?
By vanilla policy gradient, I think what is meant is normally any arbitrary policy gradient for the purposes of formalization(or whatever is trying to be communicated).

For example, let $J(\theta)$ be any policy objective function. Then our policy gradient would be $\begin{equation} \nabla_\theta J(\theta)  \end{equation}$ where the change in our policy is $\Delta \theta = \alpha \nabla_\theta J(\theta)  $ with $\alpha$ being our step size.

This will, of course, vary as notational convention and term definition can change between practitioners.